Determining axes, axial planes, and sections of macroscopic folds using computer-based methods

Abstract

The fold-axis is the eigenvector associated with the smallest eigenvalue of a symmetrical 3 × 3 matrix of direction cosines of poles to the folded surface, only if the fold is cylindrical. Cylindricity can be tested using either a χ2 or an F test. Sections showing the traces of macroscopic surfaces and of the axial plane may be constructed with the aid of computer plots that show the projection of each outcrop as well as the trace of the folded surface. The orientation of the axial plane can be calculated from the orientations of the fold-axis and the trace of the axial plane on a section normal to the fold-axis. These numerical procedures are illustrated by an analysis of four folds from the Rocky Mountains.